The periodic back and forth movement of a pendulum can be modelled as a circular rotation with constant angular velocity. We "know" that it just goes over and back so we "know" that the circular motion is just a model. All the same, maybe in the future, they'll figure out that pendulums actually move in 4 dimensions. Then they'll look back at us and think "surely they should have known that pendulums really moved in 4 dimensional circles, because they knew about this model".

I'd imagine it's similar looking at the sky. If you "knew" the motion of the planets was related to some Gods moving around, you might expect that circular motion was just a model there too.

The most likely reason was because there was an obvious correlation between astronomical events and things that happened on earth. The most obvious are seasonal weather events, which are obviously important for agriculture. Having noticed that these earthly events correlated with certain astronomical events, it was natural to extend this to predicting other events based on astronomical "omens" such as conjunctions, risings, stationary points and so on. It is likely that Babylonian rulers used astrologers when making decisions such as the best time to attack a neighbour.

I heard (iirc in the “In our time” podcast) that they associated rare/unusual cosmological events (say, a solar eclipse) with signs from the gods. Hence, to better read the signs, you want to know what's normal/predicted.

Don't quote me on this, though :)

We know that, at various times, explanation was a strictly and vigorously defended priestly prerogative, and encroaching on that was a good way to get oneself dragged behind a chariot all through town.